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9:35 AM
Looking at the result and how it is typeset, one naturally guesses that it is from Rings of Continuous Functions by Gillman and Jerison. google.com/books/edition/Rings_of_Continuous_Functions/…
 
 
6 hours later…
3:34 PM
@MartinSleziak That's right. I was objecting to "never has a countable cofinal subset". This is not true when the set of infinitely small elements of $C/P$ is empty. This can happen when $C/P\cong \mathbb{R}$.
 

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